In this study, an induction motor (IM) drive based on speed-sensorless predictive torque control (PTC) is designed to perform the high-performance control of the IMs by utilizing the least mean square (LMS) algorithm for the adaptation mechanism of the model reference adaptive system (MRAS). Here, the MRAS with LMS adaptation is based on the stator currents (i_sα and i_sβ) of the IM. Moreover, the rotor fluxes (φ_rα and φ_rβ) are obtained by the current model, which requires the rotor mechanical speed (ω_m) along with i_sα and i_sβ. In contrast to the other MRAS based studies using proportional-integral (PI) in the adaptation mechanisms to estimate state or parameter, it is possible to determine the states and/or parameters as weight coefficients in the MRAS with LMS adaptation which are calculated and updated in each iteration. Here, ω_m value is estimated and updated in each iteration as weight coefficient. Furthermore, the MRAS with LMS adaptation is compared to the MRAS using conventional PI in simulations. The simulation results clearly visualize both the estimation performance of stator current based MRAS using LMS adaptation and the effectiveness of the proposed PTC based IM drive.